4. Consider the following tests: n-th Term , Integral, Direct Comparison, Limit Comparison, Ratio, Root, and Alternating Series. In each series below, explain whether each test is applicable or why the test does not apply. If the test is applicable, explain what conclusion you can draw from that test. Also, if the series converges, state if the series is absolutely convergent or conditionally convergent. sin(e")+1 (a) Σ (c) (e) Σ, r > 0 2n+(-1)" n3+1 n=1 ( d ) Σ μ n+1 (b) Σ -Η" n%=D1 n=1

Q: Please do and explain d and e.

A:

Q: 14. The vectors a and b are such that |a| = 3, |b| = 5 and a. b = -14, then |a – b| = %3D A 62 B V62

A: Solution: Given vectors a and b such that a=3,  b=5 and a·b=-14

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A: We have find Equation of Envelope.

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A:

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Q: 30 to 19

A: The given figure is,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.